2016-10-13
Uncertainty Quantification of Radio Propagation Using Polynomial Chaos
By
Progress In Electromagnetics Research M, Vol. 50, 205-213, 2016
Abstract
In this paper we demonstrate how so-called polynomial chaos expansions can be used to create efficient algorithms for uncertainty quantification in some classes of problems related to wave propagation in stochastic environment. We provide an example from telecommunication.
Citation
Mattias Enstedt, and Niklas Wellander, "Uncertainty Quantification of Radio Propagation Using Polynomial Chaos," Progress In Electromagnetics Research M, Vol. 50, 205-213, 2016.
doi:10.2528/PIERM16062101
References

1. Austin, A. C. M. and C. D. Sarris, "Efficient analysis of geometrical uncertainty in the fdtd method using polynomial chaos with application to microwave circuits," IEEE Transactions on Microwave Theory and Techniques, Vol. 61, No. 12, 4293-4301, Dec. 2013.
doi:10.1109/TMTT.2013.2281777        Google Scholar

2. Cameron, R. H. and W. T. Martin, "The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals," Annals of Mathematics, Vol. 48, No. 2, 385-392, 1947.
doi:10.2307/1969178        Google Scholar

3. Chauvire, C., J. S. Hesthaven, and L. Lurati, "Computational modeling of uncertainty in time-domain electromagnetics," SIAM Journal on Scientific Computing, Vol. 28, No. 2, 751-775, 2006.
doi:10.1137/040621673        Google Scholar

4. Chen, M.-H., Q.-M. Shao, and J. G. Ibrahim, Monte Carlo Methods in Bayesian Computation, Springer, 2000.
doi:10.1007/978-1-4612-1276-8

5. Claerbout, J. F., Imagining the Earth’s Interior, Blackwell Scientific Pub., 1985.

6. Crank, J. and P. Nicolson, "A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type," Proc. Camb. Phil. Soc., Vol. 43, 50-67, 1947.
doi:10.1017/S0305004100023197        Google Scholar

7. Fock, V. A., Electromagnetic Diffraction and Propagation Problems, Pergamon Press, 1965.

8. Holm, P., "Wide-angle shift-map PE for a piecewise linear terrain finite-difference approach," IEEE Transactions on Antennas and Propagation, Vol. 55, 2773-2789, 2007.
doi:10.1109/TAP.2007.905865        Google Scholar

9. Jin, J. M., Theory and Computation of Electromagnetic Fields, Wiley, 2011.

10. Leontovich, M. A. and V. A. Fock, "Solution of propagation of electromagnetic waves along earth’s surface by the method of parabolic equations," J. Physics, USSR, Vol. 10, 13-23, 1946.        Google Scholar

11. Levy, M., "Parabolic equation methods for electromagnetic wave propagation," IET, 2000.        Google Scholar

12. Norton, K. A., "The propagation of radio waves over the surface of the earth and in the upper atmosphere," Proceedings of the Institute of Radio Engineers, Vol. 25, 1203-1236, 1937.        Google Scholar

13. Robert, C. P. and G. Casella, Monte Carlo Statistical Methods (Springer Texts in Statistics), Springer-Verlag New York, Inc., 2005.

14. Smith, R. C., "Uncertainty quantification: Theory, implementation, and applications," Computational Science and Engineering, 2013.        Google Scholar

15. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Ed., Artech House, Jun. 2005.

16. Tapper, F. D., "The parabolic approximation method," Wave Propagation and Underwater Acoustics, Vol. 70, 224-287, 1977.
doi:10.1007/3-540-08527-0_5        Google Scholar

17. Wan, X. and G. E. Karniadakis, "An adaptive multi-element generalized polynomial chaos method for stochastic differential equations," Journal of Computational Physics, Vol. 209, No. 2, 617-642, 2005.
doi:10.1016/j.jcp.2005.03.023        Google Scholar

18. Wiener, N., "The homogeneous chaos," American Journal of Mathematics, Vol. 60, No. 4, 897-936, 1938.
doi:10.2307/2371268        Google Scholar